How to rotate with two reference points?
Put the 3D cursor where you want the pivot of your rotation to be. This is easiest to do if you already have a vertex there, which in your case you do. go into edit mode, select the desired vertex, SHIFT + S, then 'Cursor to Selected' or 'Cursor to Active'.
Set your pivot point to 3D cursor. This can be done with . or in the UI.
Set your snap settings to the following. The important parts are Snap to Vertex, Snap with Active, and Affect Rotate in your case. Make sure snap is turned on.





Go into edit mode of the plane you want to rotate. Select everything by hitting A. Deselect and then reselect your 'active' vertex, which is the part you want to align. 
Hit R to rotate. The plane should rotate so that a line from the 3D cursor (pivot point) through the active vertex now points to the vertex closest to your mouse cursor.